What is the range in math?

The range is a measure of spread in a data set — it tells you how far apart the largest and smallest values are. It is defined as the difference between the maximum value and the minimum value: range = max − min. For example, in the data set {3, 7, 12, 20}, the range is 20 − 3 = 17. A larger range means the data is more spread out; a smaller range means the values cluster together.

How do you calculate the range of a set of numbers?

Calculating the range takes two steps: first, identify the largest number in the data set; second, identify the smallest number; then subtract the smallest from the largest. For the data set {4, 8, 15, 16, 23, 42}, the maximum is 42 and the minimum is 4, so the range is 42 − 4 = 38. That's all there is to it — the range is one of the simplest statistical measures to compute.

What is the difference between range and interquartile range (IQR)?

The range uses only the two most extreme values (max and min), which makes it sensitive to outliers. The interquartile range (IQR) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1), capturing the spread of the middle 50% of the data. For example, in the data set {1, 5, 6, 7, 8, 9, 100}, the range is 99 — heavily influenced by the outlier 100 — while the IQR may be only around 3. For skewed data or data with outliers, IQR is often a better measure of spread.

When is range a useful statistic?

Range is most useful when you need a quick, simple summary of how spread out a data set is, especially when the data has no outliers and is roughly symmetric. It is commonly used in quality control (checking whether measurements stay within acceptable bounds), weather reporting (daily temperature range), sports (score ranges over a season), and classroom settings where simplicity matters. When outliers are present or the distribution is heavily skewed, standard deviation or IQR provide more robust measures of spread.

What does a large range indicate about a data set?

A large range indicates high variability — the data values are spread far apart from one another. This could mean the data set is diverse (e.g., a class with both very high and very low test scores), contains outliers, or reflects a naturally wide distribution (e.g., incomes in a large population). A small range indicates the values are tightly clustered, suggesting low variability or a homogeneous group. However, range alone does not tell you how the data is distributed within those bounds — two data sets can have the same range but very different distributions.

How is range related to standard deviation?

Both range and standard deviation measure the spread of a data set, but standard deviation accounts for every value, not just the extremes. For normally distributed data, the range is roughly 4 to 6 times the standard deviation (the "range rule of thumb" estimates σ ≈ range / 4). This approximation is useful when you only know the range and need a rough estimate of standard deviation. However, for small samples or skewed distributions, this rule of thumb is less reliable.

Why is range sensitive to outliers?

Range is computed from only two values — the maximum and minimum — so a single extreme outlier can dramatically inflate it. For example, salary data {$40K, $45K, $50K, $55K, $500K}: the range is $460K even though 80% of salaries cluster within $15K. The IQR (interquartile range) is much more robust because it ignores the top 25% and bottom 25% of values. For quality control where outliers indicate real problems, range is intentionally sensitive. For typical data description, prefer IQR or standard deviation.

How is range used in quality control?

In statistical process control (SPC), the range of small samples (called the subgroup range) is plotted on an R-chart to monitor manufacturing consistency. If a machine is producing parts with normally sized ranges, the process is in control. A sudden jump in range signals increasing variation — perhaps a worn tool or loose fixture. The X̄-R chart (combining mean and range) is one of the most widely used quality control methods in manufacturing, popularized by Walter Shewhart in the 1920s.

Range Calculator — Find the Range of a Data Set

Calculates the range (max minus min), maximum, minimum, count, and mean of any data set.

How to Use the Range Calculator

This range calculator finds the range, maximum, minimum, count, and mean of any set of numbers instantly — enter your numbers separated by commas or spaces, for example 4, 8, 15, 16, 23, 42. There is no limit to how many numbers you can enter, and the list can include negative numbers and decimals. For a fuller statistical summary including median and mode, see our mean, median, and mode calculator.

The result updates as you type, so you can quickly test different data sets. Use the Share button to copy a link with your current numbers pre-filled — useful for sharing or saving your work.

What Is the Range Formula?

The range formula is straightforward:

Range = Maximum − Minimum

To find the range, scan your data set for the largest value (the maximum) and the smallest value (the minimum), then subtract. For the data set {2, 9, 14, 5, 21}, the max is 21 and the min is 2, so the range is 21 − 2 = 19.

This single number summarizes the total spread of your data from its lowest point to its highest point. The range is a quick and easy measure of variability — but it reacts strongly to outliers because it depends entirely on the two most extreme values.

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Range vs. Other Measures of Spread

Range is just one of several ways to measure how spread out data is. Here is how it compares to the other common options:

Range — max minus min. Fast and simple, but heavily influenced by outliers. Best for clean, symmetric data with no extreme values.
Interquartile range (IQR) — the spread of the middle 50% of the data (Q3 − Q1). More robust to outliers than range. Commonly used in box-and-whisker plots.
Standard deviation — measures the average distance of each value from the mean. The most widely used measure of spread in statistics, especially for normally distributed data. See our standard deviation calculator for details.
Variance — the square of the standard deviation. Useful mathematically but harder to interpret intuitively because it is in squared units.
Mean absolute deviation (MAD) — the average of the absolute differences from the mean. More resistant to outliers than standard deviation and expressed in the same units as the data.

As a rule of thumb, use range for a quick overview, IQR when your data has outliers, and standard deviation when you need a rigorous statistical measure for inference or comparison.

Real-World Uses of Range

Range appears in many everyday contexts where a quick measure of spread is needed:

Weather — the daily temperature range (high minus low) tells you how much temperatures fluctuate during a day. A range of 5°F is mild; a range of 40°F is dramatic.
Finance — the 52-week high/low range of a stock price summarizes its price volatility over the past year in one simple comparison.
Manufacturing and quality control — control charts track the range of measurements in a production batch to detect process drift before defects occur.
Education — a teacher might report that test scores ranged from 54 to 98 (range = 44) to describe how spread out the class performance was.
Sports — a basketball player's point totals might range from 6 to 45 over a season, indicating high game-to-game variability.

Step-by-Step Example

Problem: Find the range of the data set: 13, 7, 29, 4, 18, 22.

List the values: 13, 7, 29, 4, 18, 22
Find the maximum: 29
Find the minimum: 4
Subtract: Range = 29 − 4 = 25

The range is 25. This tells you the data spans 25 units from the smallest to the largest value. The mean is (13 + 7 + 29 + 4 + 18 + 22) / 6 = 93 / 6 = 15.50, and the count is 6.

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Range Rule of Thumb for Standard Deviation

For roughly bell-shaped (normal) distributions, there is a useful approximation called the range rule of thumb:

σ ≈ Range / 4

This estimates the standard deviation from the range. For example, if your data ranges from 10 to 50 (range = 40), the estimated standard deviation is about 40 / 4 = 10. This approximation works best for large samples from symmetric distributions and becomes less reliable with skewed data, small samples, or heavy outliers. Use it as a sanity check — if your computed standard deviation is much larger or smaller than range / 4, check your data or calculation for errors.

Sources & References

Statistics: Range — Khan Academy
Measures of Spread — Stat Trek

Range Calculator